Game-Theoretic Analysis of Bankruptcy and Taxation Problems: Recent Advances

Thomson, William

doi:10.1142/s0219198913400185

“…In the bankruptcy literature, it is typically assumed that i∈I c i ≥ E and a division rule is defined as a function that associates with each such (c, E) a vector y ∈ R I + such that i∈I y i = E and y i ≤ c i for every i ∈ I. For surveys of the literature on bankruptcy problems, we refer the reader to Thomson (2003), Thomson (2013), and Thomson (2015).…”

Section: Bankruptcy Rulesmentioning

confidence: 99%

Decentralized Clearing in Financial Networks

Csóka

¹

,

Herings

²

2018

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We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. Abstract We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules.A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure.

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“…In the bankruptcy literature, it is typically assumed that i∈I c i ≥ E and a division rule is defined as a function that associates with each such (c, E) a vector y ∈ R I + such that i∈I y i = E and y i ≤ c i for every i ∈ I. For surveys of the literature on bankruptcy problems, we refer the reader to Thomson (2003), Thomson (2013), and Thomson (2015). 1 Since we will also encounter situations where the value of the estate surpasses the sum of the claims, we define a division rule as follows.…”

Section: Bankruptcy Rulesmentioning

confidence: 99%

Decentralized Clearing in Financial Networks

Csóka

¹

,

Herings

²

2016

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We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules. A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure. Abstract We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. We assume the primitives to be denoted in some unit of account. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. We present a convenient representation of bankruptcy rules.A clearing payment matrix is a payment matrix consistent with the prevailing bankruptcy rules that satisfies limited liability and priority of creditors. Both clearing payment matrices and the corresponding values of equity are not uniquely determined. We provide bounds on the possible levels equity can take. We analyze decentralized clearing processes and show the convergence of any such process in finitely many steps to the least clearing payment matrix. When the unit of account is sufficiently small, all decentralized clearing processes lead essentially to the same value of equity as a centralized clearing procedure. As a policy implication, it is not necessary to collect and process all the sensitive data of all the agents simultaneously and run a centralized clearing procedure.

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“…The central question is how this estate should be divided over the claims and the axiomatic approach has provided firm underpinnings for a number of well-known division rules. See Thomson (2003), Thomson (2013), and Thomson (2015) for an overview of this stream of the literature.…”

Section: Introductionmentioning

confidence: 99%

An Axiomatization of the Proportional Rule in Financial Networks

Csóka

¹

,

Herings

²

2016

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The most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many bankruptcy problems are characterized by network aspects and default may occur as a result of contagion. Indeed, in financial networks with defaulting agents, the values of the agents' assets are endogenous as they depend on the extent to which claims on other agents can be collected. These network aspects make an axiomatic analysis challenging. This paper is the first to provide an axiomatization of the proportional rule in financial networks. Our two central axioms are impartiality and non-manipulability by identical agents. The other axioms are claims boundedness, limited liability, priority of creditors, and continuity. AbstractThe most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many bankruptcy problems are characterized by network aspects and default may occur as a result of contagion. Indeed, in financial networks with defaulting agents, the values of the agents' assets are endogenous as they depend on the extent to which claims on other agents can be collected. These network aspects make an axiomatic analysis challenging. This paper is the first to provide an axiomatization of the proportional rule in financial networks. Our two central axioms are impartiality and non-manipulability by identical agents. The other axioms are claims boundedness, limited liability, priority of creditors, and continuity.

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Game-Theoretic Analysis of Bankruptcy and Taxation Problems: Recent Advances

Abstract: A group of agents have claims on a resource, but there is not enough of the resource to honor all of the claims. How should it be divided? We survey the recent game theoretic approaches that have been followed in solving such "claims problems".

Cited by 34 publications

References 37 publications

Decentralized Clearing in Financial Networks

Decentralized Clearing in Financial Networks

Decentralized Clearing in Financial Networks

An Axiomatization of the Proportional Rule in Financial Networks

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